Index. ASIC, 12 see also accelerator atomic operation, 214, , 399 see also GPU atoms, 124

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1 Index A A Tale of Two Cities, , 464 abstract data type, 164 accelerator, 12, 16, 18, 28, 36 ASIC, 12 FPGA, 12 GPU, 6-7, 12, 16, 18, 28-30, 33, , , 366, 368, 370, 373, 376, 379, 390, 392, 394, 399, 404, 406, 408, 414, 418, 431, 438, 442, 444 manycore, 12 TPU, 12, 18, 358 account user, 274, 276, 286 address space, adjacency list, 164 adjacency matrix, 164, 166, 168, 172, 190, 322, 332, 334 class, 170 adjacent vertex, , 206, 208 AI Bridging Cloud Infrastructure, see AIBCI AIBCI, 36 Amazon, 7, 32 EC2, 7 Amdahl's Law, 140, 142, 144, 150, 296 Amdahl, Gene, 138, 150 Apache, 6, 32, 456 API, 24, 26, 514, 518 see also parallel programming library application programming interface, see API application specific integrated circuit, see ASIC 523 ASIC, 12 see also accelerator atomic operation, 214, , 399 see also GPU atoms, 124 B backend network, 18, 37, 226, 263, 276, 312, 316 node, 16, 227, 270, 274, 276, 286, 302, 348, 480, 484, 492, 500, 508 node name, 476, 480, 490 process, , 249, , 274, 283, 286, 348, 484 task, 228 backtrack, balanced load, 100, 102, 105, 130, 270, 274, 278, 300, 319, 382, 402 see also load balancing barrier, 23, 50, 52, 54-55, 64, 66, 76, 118, 120, 122, 132, see also thread synchronization base, 342, 344, 346, 348 benchmark dense matrix, 36 graph, 38 HPCG, 39 Linpack, 7, 36 Beowulf, 5 big CPU, 32-33, 36 big data, 32-33, 36, 456 analysis program, 488 analytics, 4, 32 climate data, 488

2 524 BIG CPU, BIG DATA big data cont. data set, 453, 464, GHCN data set, 488, 490, 492, myths, 456 NOLA data set, 498 partitioning, , 484, 494, 504 web server log, 474 binary number, 168 birds, 124 bitcoin, 32, 58, 220, 226, 232, 252 block, 32 mining, 32, 58, 136, 220, 232, 264 mining program, 220, 240, 246, 252, 256, 268, 278 bitmap, , 194 bitset, 163, 168, 170, 172, 174, 180, 190, 194, 322, 324, 342, 431 class, 170 element, 168, 170, looping over all possible, 172, 174 operation, 170, 182 reduction variable, 170 Bleak House, 464 Boolean Satisfiability, 432 branch-and-bound search, 430 breadth first search, , , 206, 208, , 334 breadth first traversal, 38 brute force search, 58 see also search bulletin board, 240 burglar, 430 byte buffer, 418, 424, 426 stream, 248 C C, 5, 24, 29-30, 361, 366, 514, 516, C++, 5, 24, 29-30, 361, 514, 520 cache, 16 friendly, 38, 420 hit, 14, 39 L1, 14, 38 L2, 13, 38 cache cont. L3, 14 L4, 14 line, 14, 38 miss, 39 carbon, 40 central processing unit, see CPU CGI, 5 Cheswick, Bill, 453 chi-square p-value, 84, 90, 92 statistic, 81-82, 84, 90 test, 80-82, 84, 90, 92, 94 chip, 6 chunk, 102, 104, , 256, , , 272, 278, 288, 290, 319, 392 factor, 104, , 278, 288, 290 size, 102, 104, tuple, , 256, 260, , , 319 Clash of the Titans, 516 class file, see Java class file class loader, see Java class loader class path, see Java class path climate data analysis program, 488, 490, 500 clock frequency, 6-7 clone, 84, 86, 92, 206 cloud computing, 7, 249 cluster, 6-7, 12, 16, 24, 32-33, 37, 48, 217, 220, 222, , 232, 236, 246, 248, 252, 262, 272, 274, 286, 296, 306, 312, 316, 319, 324, , 334, 336, 342, 346, , 482, 484, 490, 492, 504, 508, 518 utilization, 296 combinatorial optimization problem, 430 combiner, see map-reduce Comma Separated Value, see CSV command, 220 command line, 60, 106, 164, 232, 302, 332, 476 argument, 46, 48, 53, 84, 112, 130, 143, 190, 208, 222, 227, 232, 241, 256, 302, 322, 324, 344,

3 Index 525 command line cont. argument cont. 390, 406, 438, 440, 442, 464, 476, 490, 492, 498, 518 communication, 318 inter-task, 240, 242, 245, 249, 252, 258, 263, 268, 288, 300, 302, 306, 312, 316, 318, 331 interprocess, 26, 86, 220 link, 198 message passing, 23-24, 26-28, 268, 278, , 301, 319 RMI, 23 RPC, 23 tuple space, 23, 26, , , , 252, 254, 256, 258, 263, 268, 276, 288, 301, , 336, 344, 474, 484, 502, 510 compare and swap, see GPU atomic CAS composite, 340, 342 computation, 318 partitioning, 70, 300, 376, 399 rate, 137, 144, 151, 319 section, 118, 120, 143 speed, 137 to communication ratio, 284, 318, 324 computation speed, see computation rate computational kernel, 28, 358, 390, 399, 406 see also GPU computational thread, 116, 119 Compute Unified Device Architecture, see CUDA computer games, 6 computer generated imagery, see CGI concordance, 457, 459, 464 program, , 464, 476, 488, 500 conjugate gradient, 39 console, 228, 276 constructor no-argument, 245, 248, 288, 302, 500 constructor expression, 164, 182, 190, 208, 332, 438, 440 context switch, core, 12-13, 23-24, 28-29, 36, 46, 48, 50, 52-55, 66, 70, 74, 86, 104, , 128, , 140, 143, 150, , 158, 186, 200, , 220, 224, , 232, 236, 252, 256, 260, 262, 272, 274, 280, 290, 294, 296, 310, 312, 316, , 322, 324, 332, 336, 342, 357, 361, 392, , 494 hyperthreaded, 12, 14 coupled, 240 coupling, 22 loosely coupled, 22-23, 26, 249 medium coupled, 249 tightly coupled, 22-23, 26-28, 46, 249, 302, 312, 318 uncoupled, 22-23, 26, 28, 240 cover, 163, 166, 168 see also vertex cover CPU, 7, 12, 16, 18, 28-30, 33, 39, 170, 182, 214, 360, 362, 368, 376, 399, 404, 406, 408, 414, 418 chip, 7, 14, 36, 43 clock frequency, 6-7 core, 370, 390 cycles, 41 main memory, memory, 362, 366, 442 register, 214 speed, 268 thread, 28 time, 195 cryptographic application, 32 cryptography, 348 CSV, 498 CUDA, 29-30, 356, 358, , 366, , 416, 514 binary file, , 386 compiler, 361, 366, , 386, 416 compute capability, 400, 402, 406 driver, 360, 372 module file, 366, 368 program, 361

4 526 BIG CPU, BIG DATA cycle, 198 Hamiltonian, , 201, 206, 208, 210, , 215, , 334 D dart, 70, 74, 136, 143, 278, 376, , 382, 385, 390 dartboard, 70, 136 data partitioning, 23-24, 300, 302, 306, 319 data set high dimensional, 33 KDD Cup 1999, 33 data structure, 41, , 172 memory lean, 41 data-dependent branching, 28 database, 483 David Copperfield, 464 decision problem, 198, 444 deep copy, 84, 86, 92, 206, 246 dense matrix, density, see graph density depth first search, , 206, 208, , 334 derivative, 312 DGX SaturnV Volta, 40 Dickens, Charles, 456, 464, 472 Diehard, 80 Diffie-Hellman key exchange, 348 digest, see hash function digest digital currency, 58 see also bitcoin disk, 116, , 484, 494, 504 interface, storage, 473 distance Euclidean, 124 distributed computing, 4 distributed memory, 16, 18, 22, 24, 28, 220, 286, 300, 331 see also parallel program division, 342 DNS, 482 dodecahedron, 198 Domain Name System, see DNS Dubai International Airport, 488 dynamic programming, 430 dynamic schedule, 102, , 112, 120, 143, 203, 252, 278, 288, 290 E early loop exit, 60, 62, 259 ebay, 32 edge, , 166, 168, 170, 182, 187, 191, , 210, 212, 334 see also graph edge edge list, 166 efficiency, , 140, 143, , 154, 156, 158, 176, 180, 192, 260, 274, 280, 283, 294, 306, 310, 316, 318, 324, 394 see also parallel program metrics limit, 140, embarrassingly parallel, see massively parallel energy, 40 energy efficiency, equilibrium state, 124, 126, 153, 398 Eratosthenes, 342 see also Sieve of Eratosthenes Ethernet, 5, 18 Euclidean distance, 124 Euler totient, 98, 114, 278, 280, 284 exception, 46 exhausive search, 187 exhaustive search, 163, 166, 186, 188, 199, 324, 330, 430 see also search program, , 203 existing object reuse, 170, 178, 180 F Facebook, 4, 32-33, factor, 46, 98, 340, 348 field instance, 206, 214 static, 204, 206, 208, 214 field programmable gate array, see FPGA FIFO, 236 file, 116 image, 116 input, 274, 276

5 Index 527 file cont. output, 276, 286, 296 PNG, 112, 122, 143, 286, 288, 290, 494, 500 system, 229 finish rule, , 268, 270, 272, 332 first-in-first-out, see FIFO fish, 124 fixed schedule, 72, 100, 102, , 130, 252, 254, 262, 270, 272, 274, 278, 319, 518 floating point arithmetic, 306 operation, 36, 40 floating point operations per second, see flops flops, 36, 39 gigaflops, 36 petaflops, 36, teraflops, 36 flops per watt, 40 gigaflops per watt, 40 fluid dynamics, 39 Fortran, 5, 24, 29, 361, 514, 520 fossil fuels, 40 FPGA, 12 see also accelerator fractal, 110 frontend node, 18, 226, 228, 236, 248, 270, 274, 276, 286 process, 228, 249, , 283 function minimum, 312 functional unit, 13 G galaxy, 124 garbage, 176 collection, 178 collector, 176 gather thread, 288 Gelernter, David, 240 General Public License, see GNU GPL generic class, 418, , 466 genetic algorithms, 186 Geographic Information System, see GIS GHCN, 488 data set, 488, 490, 492, gigaflops, 36 gigaflops per watt, 40 GIMPS, 340 see also prime GIS, 498 Global Historical Climatology Network, see GHCN global variable, 60, 62, 70, 72, 74, 76, 90, 92, 112, 130, 172, 174, , 208, , 270, 390, 392, 442, 508, 516 global warming, 40, 495 Gmail, 4 GNU GPL, 236 Gold Rush, 58 Google, 4, 32-33, 488 GPU, 6-7, 12, 16, 18, 28-30, 33, , , 366, 368, 373, 376, 379, 390, 394, 399, 404, 406, 408, 414, 418, 431, 438, 442, 444 see also accelerator acceleration, 361 accelerator, 370, 390, 392, 442, 444 atomic add, 410 atomic addition, 402, 404 atomic CAS, 410, 436 on floating point values, 410 atomic operation, , 399 barrier, block, 358, 360, 362, , 373, 376, , , 387, , 402, 406, 408, 416, 434, 442 dimension, , 368, 382 index, , 382 card, , 360, 390 chip, 353 computation partitioning, 382, 399 computational arc, 28, 362 computational grid, 358 compute capability, 366, , 376, 385, 387 core, 319, 358, 360, 399, 431 global memory, , 366, 376,

6 528 BIG CPU, BIG DATA GPU cont. global memory cont. 378, 386, 400, 404, 406, 420, 422, 434, 436, 438, 442 variable, 360, , 382, 386 global variable, grid, 358, , , 376, , 382, 399, 402, 406, 434, 436 dimension, 364, 368, 382 kernel, 28-29, 358, 360, 362, 368, 370, 376, , 387, 390, 392, 399, 404, 406, 408, 416, 434, 438, 442 kernel function, 28, 30, 358, , 364, 366, , 379, 382, 387, 402, 416, 418, 422, 434, 436, 442 kernel interface, 366, 368, 378, 404, 418, 440 kernel method, 366, 368, 370, , 392, 404, 406, 440 kernel object, 368, 370 L1 cache, 358, 370, 406, 420 L2 cache, 358, 420 main program, 366 memory, 362, 406, 418, 426 mirrored variable, 362, 378, 380, 386, 404, 406, 410, 418 module, 378, 406, 442 module object, 368 multiprocessor, , 360, 370, 373, 376, 380, 387, 399, 406 object, 366, 368, 378, 386, 392, 406, 442 program, 358 reduction, , , 404, 408, 416, 434, 436 tree, , 404 register, 358, 373, 387 shared memory, 358, 360, 370, 378, 380, 383, 387, 400, 404, 406, 416, 434 variable, 360, 380, 382 structure, 422 array, 426 GPU cont. structure cont. class, 424, 426 field, 422, 424 matrix, 426 padding, 422, 424 thread, 28, 358, , 364, 373, 376, 378, 380, , 387, , 404, 406, 408, 434, 436, 442 index, , 382, 384 position in grid, 364 thread block, 358 thread rank, 402 variable, , 426 graph, 37, , 166, 172, , 191, , 204, 206, 208, 210, , 324, 328, 330, 332, 334 analytics, 39 breadth first traversal, 38 constructor expression, 332, 334 cycle, 198 data structure, 164 adjacency list, 164 adjacency matrix, 164, 166, 168, 172, 190, 322, 332, 334 edge list, 166 density, 187 edge, matrix, 37 path, , 204, 206, 208, 210, 330, 332 random, , 182, 187, 192 shortest paths, 38 sparse, 38 spec, 163, 170, 172, 190, 324 class, constructor expression, 164, 322 interface, object, , 172, 190 theory, 162, 198 traversal, 38 vertex, adjacent, , 206, 208 graph specification, see graph spec Graph500 List, 37-38

7 Index 529 graphic, 502, 504, 508 class in PJ2 Library, 502 file, 500, 502, 504 viewing, 502 graphical user interface, see GUI graphics processing unit, see GPU Great Internet Mersenne Prime Search, see GIMPS Green500 List, 40 GUI, 276 guided schedule, 104, , 278, 280 Gustafson, John, 150, 152 H Hadoop, 6, 32, 456, 460, see also map-reduce library, parallel programming library Hamilton, Sir William Rowan, 198 Hamiltonian cycle, , 201, 206, 208, 210, , 215, , 334 program, , 208, 210, 331 Hamiltonian Cycle Problem, , 203, 330 Hamming, Richard W., 490, 495 hard problems, 186 hash function, 32, 58, 60, 95 digest, 58, 60, 222 hash table, 458, 466, 484 heartbeat message, hectoprime, 340 see also prime heuristic, , 190, 431 heuristic search, 186, 322, 324, 431 see also search program, , 203 High Perforance Computing, see HPC High Performance Conjugate Gradient, see HPCG Highly Parallel Computing Benchmark, 36 histogram, 82, 84, 86, 90, 92, 94 reduction variable, 82, 84, 86, 94 HPC, 514 HPCG, 39 see also benchmark HSB, 504 hue, 110, 504 Hue-Saturation-Brightness, see HSB Hulu, 32 hyperthreaded, 23 see also core I I/O, 151 section, 118, 120, 143 thread, 116, 119, 286, 288 IBM, 7, 18 Icosian Game, 198 ideal sizeup, 151 ideal speedup, 114, 119, , 140 image, 110 file, 116 queue, 288 row, 286, 288, 290 in stream, 246 see also streamable object incomplete gamma function, 94 Infiniband, 18 initial state, 124 input file, 274, 276 insect swarms, 124 instance field, 206, 214 instruction unit, 13 integer, 168, 180, 182, 194, 340 bitwise Boolean operation, 170, 182 functional unit, 170, 182 Intel, 43 Xeon 5600, 43 Xeon E5-2696, 370 inter-task communication, 240, 242, 245, 249, 252, 258, 263, 268, 288, 300, 302, 306, 312, 316, 318, 331 interacting tasks, 258 Internet, 18, 98 node, 453 Internet Protocol, see IP interprocess communication, 26, 86, 220 IP, 5 address, , 480, 482 IPC, see interprocess communication iterative, 202

8 530 BIG CPU, BIG DATA iterator, 163 J JAR, Java, 6, 24, 26, 30, 361, 366, 456, 514, 516, class file, , 372 class loader, 229 class path, 229 compiler, 361, 366 iterator, 163 Object Serialization, 248 package, 368 Reflection, 182, 466 Java archive, see JAR Java Development Kit, see JDK Java Native Interface, see JNI Java Virtual Machine, see JVM JavaScript Object Notation, see JSON JDK, 514 JIT compiler, 144, 180, 372, JNI, 30, 361, 386 job, 220, 222, , 236, , 248, 263, 274, 286, 296, 302, 319, 331, 342 class, 222, 224, 226, 228, 232, 254 command line argument, 280 main method, , 256, , 268, 270 main program, 252, 254, 272, 288, 302, 319, 322, 332, 344 object, 248 process, 226, , 270, 276, 278, , 322, 348 running in, 270, 274, 276, 286, 288, 290, 302, 492, 500, 508 work queue, , 334, 336 JSON, 457 JUQUEEN, 38 just-in-time compiler, see JIT compiler JVM, 50, 143, 176, 214, 249, 348, 372, 519 heap, 176, 249, 484 interpreted, 519 maximum heap size, 484 K K Computer, KDD Cup 1999 data set, 33 see also data set Keeneland, 33 kernel, 28-29, 358, 360, 362, 368, 370, 376, , 387, 390, 392, 399, 404, 408, 416, 434, 438, 442 see also GPU function, 390 interface, 390 launch, 362, 370 kernel function, 28, 30, 358, , 364, 366, , 379, 382, 387, 402, 416, 418, 422, 434, 436, 442 see also GPU argument, 364, 366, 382 local variable, 373, 382 kernel interface, 366, 368, 378, 404, 418, 440 see also GPU kernel method, 366, 368, 370, , 392, 404, 406, 440 see also GPU kernel object, 378 knapsack, 430 Knapsack Problem, , 444 algorithm branch-and-bound search, 430, 442 dynamic programming, 430 exhaustive search, 430, 442 data structure, 431 high precision, , 446 parameters, 438, 440, 442 problem spec, 438 interface, 438, 440 object, 440, 444 program branch-and-bound search, 444, 446 exhaustive search, 444, 446 heuristic search, 444, 446 solution, 434, 436 class, 440, 442 optimum, 442 quality, 442, 444, 446

9 Index 531 Knapsack Problem cont. solution cont. reduction variable, 440, 442 strongly correlated, 440 weight-value class, 438 weight-value structure, 432, 434, 436 L L1, see cache L2, see cache L3, see cache L4, see cache LAMMPS, 33 Large Scale Atomic/Molecular Massively Parallel Simulator, see LAMMPS latency hiding, 16 Launcher, , 348 leapfrog schedule, , 232, 236, 252, 256, 259, 263, 278, 382, 402 linear equations, linked data structure, 28 LinkedIn, 32 Linpack, 7, 36 see also benchmark Linux, 5, 518 Lisp, 5 little CPU, 32, 456 little data, 32 load balancing, 102, , 110, 112, , 278, 280, 284, 288 coarse-grained, 278 fine-grained, 278 local variable, 176, 178 lock, see also thread synchronization log-log plot, 138 Lonestar, 514 long integer, 181, 194 loop, 46, 60, 84 early exit, 60, 62, 259 iteration, 48-49, 301 parallel, 49-50, 52-55, 60, 62, 66, 72, 82, 90, 92, 98, 100, 104, 112, , , 130, 132, 134, 143, 158, 163, 172, 174, 186, loop cont. parallel cont. 190, , 208, 210, 232, , 259, 280, 283, 304, 319, 334, 398, 478, 510 sequential dependency, 49, 98, 110, 322, 398 loosely coupled, 22-23, 26, 249 see also coupling M machine code, machine instruction, 170 machine learning, 33 main memory, 12-13, , 319, 473, 484 main method, 222 main program, 208 main thread, 112, 116, , 122 makespan, 48 Mallory, George, 348 Mandelbrot Set, 110, 112, 114, 127, 136, 286 program, 138, 140, , 286, 296, 300 Mandelbrot, Benoit, 110 manycore, 12 see also accelerator map-reduce, 4, 6, 32-33, 456, , 488 combiner, , 464, 466, 468, , 478, 480, , 492, 494, 500, 502, 508, 510 customizer, 476, 478, 480, 492, 500, 502, 508, 510 job, 464, 473, 475, 478, 484, 498 main program, 474 key-value pair, 457, , 464, 466, 474, 476, 478, 480, , 490, 492, 500, 502, 504, 510 library Hadoop, 6, 32, 456, 460, PJMR, 33, 456, , 466, 474, main program, 461

10 532 BIG CPU, BIG DATA map-reduce cont. mapper, 457, , 464, , 478, 482, 485, 492, 500, 502, 508 map() method, 462, 464, 478, 480, 492, 500, 508 multiple objects, 474, 480, 494 task, 464, , 476, 478, 480, 484, 490, 492, 500, 508, 510 thread, 476 parallel program, 459 program, 460, 484, 495 record, , , 474, 478, 490, 492, 500, 508 reducer, 459, , 464, , 476, 480, 492, 494, 500, 502, 510 reduce() method, 462, 464, 480, 494, 502, 504, 510 task, 464, , 476, 478, 480, 484, 492, 494, 500, 502, 508, 510 source, 457, , 464, , 476, 478, 490, 492, 500, 508, 510 directory, 492, 500 text file, 461 workflow, , 466, 472 mapper, see map-reduce massively parallel, 220, 232, 240, 252, 322, 356, 390 massively parallel randomized approximation, see MPRA massively parallel stochastic local search, see MPSLS master, 256, , 263, 268, 270, 278, 283, 288 schedule, 272 master task, 252 master-worker, , 256, , 262, 268, 270, 278, 284, 286, 288, 322 pattern, 263, 300 matching tuple, , 248, 260, 264, 302, 304, 342, 346 matrix, 356, 358, 362, , 368, 376 dense, equation, 36 graph, 37 sparse, 37, 39 medium coupled, 249 see also coupling medium CPU, 33 megaprime, 340 see also prime search, 340 megawatts, 40 memoization, 344 memory, 220, 249, 286 memory lean data structures, 41 memory wall, 39 Mersenne prime, 5, 340 see also GIMPS message, 24, 26, 318 inter-node, 24 intra-node, 24 message passing, 23-24, 26-28, 268, 278, , 301, 319 see also communication Message Passing Interface, see MPI metric, 137 metrics, 136 middleware, 46, 50, 54, 92, 94, , 236, 246 minimum vertex cover, , 172, 174, , 190, 192, 194 program, 164, 166, 172, 190, 431 Minimum Vertex Cover Problem, , , 198, 322 Mira, 38 modular exponentiation, 342 molecular dynamics, 33 Monte Carlo integration, 514 Moore's Law, 6 Mount Everest, 348 MPI, 5, 23, 26, 249, , 514, 519 see also parallel programming library MPRA, 186, 431 algorithm, 322 program, 186, 188, 190, 322

11 Index 533 MPSLS, , 446 multicore, 4-6, 14, 18, 23, 28, 32, 37, 43, 163, 172 multiple thread safe, 112, 116, 120, 508 multithreaded program, 24, 232 Myrinet, 18 myth big data = map-reduce, 456 C is faster than Java, 514, 519 map-reduce = Hadoop, 456 N N-body problem, 124, 514 program, 124, 127, 300, 318, 398 simulation, 408 National Climatic Data Center, see NCDC National Oceanic and Atmospheric Administration, see NOAA NCDC, 488, 494 nested class, 224, 232 network, 198 backend, 226, 263, 276, 312, 316 communication, 249, 312, 324 interface, 12, 276 intrusion, 33 speed, 268 New Orleans, 498, 504 no-argument constructor, 245, 248, 288, 302, 500 NOAA, 488 node, 7, 12, 16, 22-24, 27, 37, 48, 198, 220, 222, , 232, 236, 246, 252, 256, 259, 262, 268, 272, 280, 290, 300, 312, 319, 322, 331, 336, 342, 357, 390, 392, 431, 473, 476, 484, 494 accelerated, 356 backend, 16, 227, 270, 274, 276, 286, 302, 348, 480, 484, 500, 508 frontend, 18, 226, 228, 236, 248, 270, 274, 276, 286 multicore, 318 unaccelerated, 356 NOLA see also New Orleans data set, 498 emergency call, 498 graphic, 498 geographic coordinates, 498 PJMR job, 504 non-ideal speedup, 114, 132 non-negative least squares, 144 nondeterministic polynomial-time problem, see NP problem NP problem, , 203, 444 null hypothesis, Nvidia, 7, 18, 29, 353, 356 see also CUDA Kepler GK110, 353 Tesla C2075, 372 Tesla K40c, 356, 358, , 370, 390, 406 Tesla V100, 358 O Oak Ridge National Laboratory, 1, 7, 33, 217 object oriented design, 82, 172 object type, 414 odd prime, 340, 342, 344 list, 342, 344, 346 Oliver Twist, 464 on-demand rule, , 342, 344, 346 on-demand task, 243, 342 pattern, 348, 350 OpenCL, 29-30, 514 see also parallel programming library OpenMP, 5, 24, 514, 516, see also parallel programming library operating system, 50, 116, 360 out stream, 246 see also streamable object outer product, 356, 358, 360, 362, 370, 373, 376 program, 414 output file, 276, 286, 296 task, 286, 288, 290, 300

12 534 BIG CPU, BIG DATA output cont. tuple, 288, 290 class, 288 overhead, 52, 104, 134, 142, 151, 220, 249, 276, 278, 288, , 348, 350, 372, 385, 394, 410 overlapped computation and I/O, see overlapping overlapping, 116, 119, 138, 143 P p-value, parallel reduction tree, 76, 92, 94, 268, 276 work queue, , 206, 208, 212, , 334, 336 pattern, , , 334, 348, 350 parallel computer, 52, 66, 150, 186, 322, 514 cluster, 6-7, 12, 16, 24, 32-33, 37, 48, 217, 220, 222, , 232, 236, 246, 248, 252, 262, 272, 274, 286, 296, 306, 312, 316, 319, 322, 324, , 334, 336, 342, 346, 390, , 482, 484, 490, 492, 504, 508, 518 multicore, 50, 163, 319, 322 parallel computing, 4 application, 32 Parallel Java 2 Library, see PJ2 Parallel Java Map Reduce, see PJMR parallel loop, 49-50, 52-55, 60, 62, 66, 72, 82, 90, 92, 98, 100, 104, 112, , , 130, 132, 134, 143, 158, 163, 172, 174, 186, 190, , 208, 210, 232, , 259, 280, 283, 304, 319, 334, 398, 478, 510 body, 49-50, 60, 62, 174, 176, 178, 256, 259, 270 body object, 54, 62, 120, 204 index, 49-50, 54-55, 62, 66 index range, 64, 392 iteration, 49-50, 52, 62, 74, 90, 100, 102, 104, 107, 190, 203, parallel loop cont. iteration cont. 274 master-worker, , 256, , 262, 268, 270, 278, 284, 286, 288, 322 object, 49-50, 53, 66, 90, 120, 252, 256, 259 outermost, 263 partitioning, 64-65, 72, 102, 104, , 143, 252, 254, 256, 259, , 270, 272, 278, 286, 288, 319, 390, 402, 518 schedule, 62, 64, 66, 102, 106, 252, 280 dynamic, 66 fixed, 64, 66 guided, 66 leapfrog, 66 proportional, 66 work sharing, 518 worker, 263 worker object, 259 parallel program, 4, 6, 58, 60, 64-66, 70, 72, 74, 82, 86, 88, 90, 95, 100, 102, 110, 112, 114, 128, 130, , 144, , 156, 163, 174, 192, 194, , 203, 212, 220, 240, 346, 348, 390 big data, 456 cluster, 24, 86, 222, 236, 245, 249, , 256, 260, 268, 270, 274, 278, 284, 286, 288, 300, 312, 318, 328, 331, 334, 340, 342 computation speed, 137 distributed memory, 22, 27 efficiency, , 140, 143, , 154, 156, 158, 176, 180, 192, 260, 274, 280, 283, 294, 306, 310, 316, 318, 324, 394 GPU, 28-29, 357, 362, 376, , 399, 414 hybrid, 27-28, 232, 236, 240, 256, 259, 268, 272, 278, 300 map-reduce, 459, 498 memory, 41

13 Index 535 parallel program cont. metrics efficiency, , 140, 143, , 154, 156, 158, 176, 180, 192, 260, 274, 280, 283, 294, 306, 310, 316, 318, 324, 394 sizeup, 137, , 154, 156, 192, 274, 316, 324, 394 speedup, 52, 65-66, 74, 92, 100, 102, , 114, 116, 119, 132, , 140, 143, , 176, , 232, 236, 280, 294, 306, 310, 334, 336, 346 multicore, 54, 90, 172, 204, 208, 253, 268, 270, 278, 286, 288, 328, 330, 332, 398, 516 multithreaded, 252 overhead, 52, 104, 134, 142, 151, 220, 249, 276, 278, 288, , 348, 350, 372, 385, 394, 410 parallelizable portion, 140, , 150, 152, 156, 284, 296 performance, 40, 52, 76 problem size, 136, 142, , , 156, 186, 280, 283, 306, 310, 312, 316, 318, 385, 394, 408 running time, 36, 38, 40, 48, 76, 100, 102, , 114, 116, 119, 122, 132, , , , 154, 174, 176, 178, 180, 186, 188, 192, 203, 210, 212, 224, 274, 280, 284, 294, 302, 306, 310, 312, 316, 318, 324, 334, 336, 346, 350, , 385, 394, 408, 410, 420, 444, 480, 482, 494, 518 scalability, 180, 210, 220, 288, 318 sequential fraction, 140, 143, 150, , 156, 176, 260, 274, 283, 394 sequential portion, 140, , , 156, , 296 shared memory, 22, 24, 27 parallel program cont. weak sequential fraction, 152, 154 parallel programming, 70, 98, 514 cluster, 33, 220, 248, 361, 456, 514 GPU, 356, 361, 514 library, 24, 26, 249 CUDA, 29-30, 356, 358, , 366, , 416, 514 Hadoop, 6, 32, 456, 460, MPI, 5, 23, 26, 249, , 514, 519 OpenCL, 29-30, 514 OpenMP, 5, 24, 514, 516, PJ2, 24, 30, 32-33, 46, 76, 92, 94, 163, 170, 204, 220, 226, 236, 240, 244, , 252, 268, 274, 276, 286, 318, 331, 356, 361, 366, 370, 376, 416, 418, 422, 456, 466, 475, 483, 492, 498, 508, 514 PJMR, 33, 456, , 466, 474, multicore, 46, 220, 361, 456, 514 parallel reduction, 70, 72, 76, 82, 98, 158, 172, 186, 190, 204, 268, 280, 284, 322, 376, 442, 474, 484 see also reduction parallel section, 54, 116, , 134, 290, 442 code, 118 computation, 118, 120, 143 I/O, 118, 120, 143 object, 118, 120, 390 pattern, 116, 118 Parallel Thread Execution, see PTX parallel thread team, 50, 52-55, 62, 64-66, 74, 82, 90, 100, , 112, , 134, 143, 158, 174, 190, , 208, 210, , 215, 226, 232, 252, 256, 259, , 280, 286, 288, 330, 390, 392, 442, 510, 516, 518 parallelizable portion, 140, , 150, 152, 156, 284, 296

14 536 BIG CPU, BIG DATA partial differential equation, see PDE path, , 204, 206, 208, 210, 330, 332 pattern cloning in Java, 86 master-worker, , 256, , 262, 268, 270, 278, 284, 286, 288, 322 parallel section, 116, 118 reduction, 70, 76, 82, 98, 130, 172, 322 PC, 5-7, 217 PDE, 39 per-thread variable, 70, 72, 74, 76, 82, 88, 90, 92, 94, 98, 112, 128, , 204, 288, 322, 376, 378, 380, , 390, 392, 442, 474, 478, 484, 516 initialization, 72, 88, 120 personal computer, see PC petaflops, 36, pi, 70, 74, 80, 82, 88, 136 program, 143, 156, 270, 274, 278, 322, 376, , 390, 392, 399, 402, 404, 414, 514, 516 pigeonhole principle, 60 pixel, 110, 142 array, 122 color, 110, 112, 120, 122, 286, 288 column, 112, 127 resolution, 110 row, 112, 114, 116, 120, 127, 286, 288, 300 Piz Daint, 39 PJ2, 24, 30, 32-33, 46, 76, 92, 94, 163, 170, 204, 220, 226, 236, 240, 244, , 252, 268, 274, 276, 286, 318, 331, 356, 361, 366, 370, 376, 416, 418, 422, 456, 466, 475, 483, 492, 498, 508, 514 see also parallel programming library launcher, 48, 106, 222, 228, 254, 302, 394, 478 middleware, 46, 50, 54, 92, 94, 226, 228, 236, 246 PJMR, 33, 456, , 466, 474, see also map-reduce library, parallel programming library job, 461, 466, , 508 main program, , 478, 490, 500, 508, 510 program, 482 plot, 490, 492, class in PJ2 Library, 492, 494 file, 490, 492, 494 viewing, 494 PNG, 112 file, 112, 122, 143, 286, 288, 290, 494, 500 pointer chasing, 28 Portable Network Graphics, see PNG position, 124, , 132, , 306, , 402, 404, 406, 408, 410, 416 PostScript file, 494 primality test, 46, 54, 98, 340, 342 trial division, 46, 98, 340, 342, 344, 346 prime, 54, 340, 342, 344 factor, 98, 340, 342, 346 hectoprime, 340 infinite number of, 340 megaprime, 340 number, 46, 48, 52, 98, 340, 342 odd, 340, 342, 344 list, 342, 344, 346 Proth, 340, 342, 346, 348 uses in cryptography, 348 Prime Number Theorem, 340 PrimeGrid, 340 see also prime primitive type, 414, 422 printout, 228, 236, 276, 284, 306, 324, 334, 346, 362, , 392, 442, 462, 480, 482, 492, 502, 504, 516 PRNG, 70, 72, 80, 82, 84, 88, 90, 95, 163, 190, 270, 304, 306, , 392, 436, 516, 518 seed, 70, 72, 74, 84, 88, 95, 163, 190, 270, 304, 306, 322, 378,

15 Index 537 PRNG cont. seed cont. 382, 392, 436, 438, 440, 518 structure, 434 problem size, 136, 142, , , 156, 186, 280, 283, 306, 310, 312, 316, 318, 385, 394, 408 problem solving decoupled from problem specification, 182 problem solving cont. program, 183 problem specification, 183 class, 183 decoupled from problem solving, 182 interface, 183 process, 23-24, 27-28, 220, , 232, 246, 248, 300, 508 backend, , 249, , 274, 283, 286, 348, 484 frontend, 228, 249, , 283 proportional schedule, 104, , 278, 280, , 288, 290 prospector, 58 Proth number, 340, 342, 344, 346 prime, 340, 342, 346, 348 Proth's Theorem, 340, 346 test, 342, 344, 346 Proth, François, 340 protocol, 26 provenance, 476, 482, 492, 504 proxy object, 368 pseudorandom number, 80, 82, 95 pseudorandom number generator, see PRNG pthreads, 24 PTX, 372 assembler, 373 file, 372 pub, 385 public key cryptosystem, 98, 348 Q queue, 200, , 206, 208, 212, , 334, 336 R random graph, , 182, 187, 192, 210, 212 number, 70, 72, 74, 80, 82, 84, 88, 90, 95 permutation, 195 subset, 190, subset generator, 190, 194 Ranger, 514 rank, 53, 64-66, 72, 74, 90, 100, 120, 122, 252, 256, 260, , 270, 302, 304, 392, 434, 436, 518 record, see map-reduce recursive, 202, 206, 208 reducer, see map-reduce reduction, 70, 72, 76, 82, 98, 158, 172, 186, 190, 204, 268, 280, 284, 322, 376, 442, 474, 484 operation, 70, 72, 86, 94, , 462, 492, 500, 516 pattern, 70, 76, 82, 98, 130, 172, 322 sum-reduce, 70, 72, 74, 128, 272, 376, 390, 392, , 416, 458, 462, 500, 516 task, 268, 270, 272, 274, 276, 283, 300, 322, 324 tree, 76, 92, 94, 268, 276, , 404 variable, 70, 82, 84, 86, 90, 92, 94, 130, 163, 172, 174, 270, 276, 324, 390, 392, 442, , , 466, 468, 474, 492, 500, 516 class, 76, 82, 84, 86, 92, 94, 270, 462 register, 13, 214 relatively prime, 98, 278 remote method invocation, see RMI remote procedure call, see RPC result task, 334 Rivest-Shamir-Adleman, see RSA RMI, 23 see also communication

16 538 BIG CPU, BIG DATA RPC, 23 see also communication RSA, 98, 348 exponent, 98 modulus, 98 rule, 222, 226, 232, 236, 240, 245, 319, 332 finish, , 268, 270, 272, 332 firing, object, 222 rule cont. on-demand, , 342, 344, 346 start, 240, , 254, 256, 262, 268, 288, 302, 332, 344 running time, 36, 38, 40, 48, 76, 100, 102, , 114, 116, 119, 122, 132, , , , 154, 174, 176, 178, 180, 186, 188, 192, 203, 210, 212, 224, 274, 280, 284, 294, 302, 306, 310, 312, 316, 318, 324, 334, 336, 346, 350, , 385, 394, 408, 410, 420, 444, 480, 482, 494, 518 data, 41, 106, 138, , 154, 156, 260, 294, 310, 316 model, , 154, 176, 178, 260, 280, 294, 296, 310, 312, 316 model fitting, 142, 156 model parameters, 142, 156 S Sakura, 40 SAT, see Boolean satisfiability scalability, 180, 210, 220, 288, 318 Scalable Coherent Interface, see SCI scaling, 136, 176 strong, , 140, 144, , 156, 174, 212, 259, 286, 290, 294, 296, 306, 310, 312, 316 weak, , 144, , 156, 186, 192, 194, 220, 274, 312, 316, 324, 328, 394, 518 schedule, 62, 64, 66, 106, 252, 280 dynamic, 66 fixed, 64, 66 schedule cont. guided, 66 leapfrog, 66 proportional, 66 SCI, 18 search, 206, 208, 210, 213, 332 branch-and-bound, 430 breadth first, , , 206, 208, , 334 brute force, 58 depth first, , 206, 208, , 334 exhaustive, 163, 166, 186, 188, 199, 324, 330, 430 heuristic, 186, 322, 324, 431 stochastic local, 431 task, 332, 334 tree, Search for Extraterrestial Intelligence, see SETI search level, 206 search state, 206, 208 search tree, , 212 section, see parallel section single-threaded, 132 security, 274, 276 seed, see PRNG seed semaphore, see also thread synchronization sequential dependencies, 127, 263, 300 sequential dependency, 49, 98, 110, 322, 398 sequential fraction, 140, 143, 150, , 156, 176, 260, 274, 283, 394 sequential loop, , 132, 252, 263, 304, 334, iteration, 132 sequential portion, 140, , , 156, , 296 sequential program, 60, 64-66, 70, 72, 74, 82, 84, 90, 98, 114, , 144, 151, 174, 192, 194, 220, 224, 280, 332, 334, 346, 385, 398 sequential section, 54 Sequoia, 38 SETI, 5 SHA-256, 32, 58

17 Index 539 shallow copy, 86 shared data structure, 300 memory, 22-23, 268, 319, 331 variable, 62, 74, 112, 214, 252, 516 shared memory see also parallel program shortest paths, 38 Shoubu System B, 40 Sierra, 36, 39 sieve, 344 Sieve of Eratosthenes, 342 see also sieve SIMD, 28 simulated annealing, 186 single instruction stream multiple data stream, see SIMD sizeup, 137, , 154, 156, 192, 274, 316, 324, 394 see also parallel program metrics ideal, 151 limit, 152 slice, 128, , 304 snapshot task, 302, 306 social network analytics, 37 socket, 26, 226 source, see map-reduce sparse graph, 38 sparse matrix, 37, 39 speedup, 52, 65-66, 74, 92, 100, 102, , 114, 116, 119, 132, , 140, 143, , 176, , 232, 236, 280, 294, 306, 310, 334, 336, 346 see also parallel program metrics ideal, 114, 119, , 140 limit, 140, 144, 150, 153 non-ideal, 114, 132 Spotify, 32 spreadsheet, 32 SQL, 484 star cluster, 124 stars, 124 start rule, 240, , 254, 256, 262, 268, 288, 302, 332, 344 static field, 204, 206, 208, 214 statistic, statistical test, 80, 86 chi-square test, 80-82, 84, 90, 92, 94 stochastic local search, 431 Stone Soupercomputer, 217 stop flag, 204, 208, , , 344 stop tuple, 256, , 342, 344, 346 storage, 200, 202, 214 allocation, 300, 304, 320 streamable object, , 248, 302, 474, 484, 500 strong scaling, , 140, 144, , 156, 174, 212, 259, 286, 290, 294, 296, 306, 310, 312, 316 Structured Query Language, see SQL subproblem, , , 206, 208, 212, 330, 336 Subset Sum Problem, 444, 446 Suiren-2, 40 sum-reduce, 70, 72, 74, 128, 272, 376, 390, 392, , 416, 458, 462, 500, 516 see also reduction Summit, 1, 7, 18, 36, Sunway TaihuLight, 36, 38 supercomputer, 1, 5, 7, 33, 36, 200, 220, 514 AIBCI, 36 DGX SaturnV Volta, 40 energy efficiency, JUQUEEN, 38 K Computer, Keeneland, 33 Lonestar, 514 Mira, 38 performance, 36 Piz Daint, 39 program, 32 Ranger, 514 Sakura, 40 Sequoia, 38 Shoubu System B, 40 Sierra, 36, 39 Suiren-2, 40

18 540 BIG CPU, BIG DATA supercomputer cont. Summit, 1, 7, 18, 36, Sunway TaihuLight, 36, 38 Tianhe-2A, 36 Trinity, 39 surveillance camera, 162 system clock, 114 T table lookup, 112 tabu search, 186 target, , 260, 302, 304 task, 220, 222, , 232, 236, 240, , 246, , 252, 258, 263, 268, 270, 274, 278, 286, 288, 300, 331, 348 backend, 228 class, 224, , 232, 236, 241, , 348 command line argument, 241, 256, 348 group, 222, 256, 258, 288, 302, 319, 332 interacting, 258 main method, 256, 442 main program, 390, 418 master, 252 on-demand, 342 output, 286, 288, 290, 300 process, rank, 252, 256, 262, 270 reduction, 268, 270, 272, 274, 276, 283, 300, 322, 324 single, 256 single threaded, 330, 332, 334, 342, 346 snapshot, 302, 306 spec, 222 worker, , 256, , , 268, 270, 272, 274, 278, 280, 284, 286, 288, 290, 300, 302, 306, 312, 316, 319, 322, 324, , , 348, 350 TCP, 5, 26, 226 team thread, 92, 128 template, , 248, 258, 260, , 290, 302, 304, 306, 337, 342 class, 302 tensor processing unit, see TPU teps, terateps, 38 teraflops, 36 terateps, 38 TestU01, 80 Texas Advanced Computing Center, 514 thread, 13-14, 22-24, 27-29, 50, 52-55, 62, 64-66, 70, 72, 74, 76, 88, 100, , 112, 116, , 128, 130, 132, 134, 143, 158, 190, , 208, 210, , 215, 220, 226, 232, 252, 256, , , 268, 270, 274, 278, 280, 286, 288, 300, 319, 322, , 338, 376, 390, 392, 442, , 478, 480, 490, 494, 508, 510, 516, 518 communication, 22 computational, 116, 119 coordination, 22 gather, 288 I/O, 116, 119, 286, 288 main, 112, 116, , 122 rank, 120, 122, 270, 392, 434, 436, 518 thread pool, 134 thread synchronization, 23, 50, 62, 72, 76, 94, 116, 118, 128, , 337, , 404 thread team, 50, 52-55, 62, 64-66, 74, 82, 90, 100, , 112, , 134, 143, 158, 174, 190, , 208, 210, , 215, 226, 232, 252, 256, 259, , 280, 286, 288, 330, 390, 392, 442, 510, 516, 518 rank, 53, 64-66, 72, 74, 90, 100 thread-local variable, 62, 66, 130, 174, 270, 508 initialization, 62, 66 threshold level, , 206, 208, 212, 330, 332, 334 Tianhe-2A, 36

19 Index 541 tightly coupled, 22-23, 26-28, 46, 249, 302, 312, 318 see also coupling time step, , 130, 136, 153, 158, 302, 304, 306, 310, 312, , , 406, 408, 416 TLS, 348 Top500 List, 7, 36, 38-40, 220 totient, 98, 114, 278, 280, 284 program, 278 TPU, 7, 12, 18, 358 see also accelerator core, 358 Tracker, , 236, 256, 258, 319, 332, 348, 370, 379, 392 queue, , 236, 258, 332 scheduling policy, 236 web interface, 228 Transmission Control Protocol, see TCP Transport Layer Security, see TLS traversed edges per second, see teps trial division, 46, 98, 340, 342, 344, 346 see also primality test Trinity, 39 tuple, 86, 204, , 246, 248, 264, 268, 270, 276, 288, , 324, 331, 342, 474, chunk, , 256, 260, , , 319 class, , , 286, 302, 324, 332, 336, 344 field, , 246, 302 immutable, 246 listener, 245, 258, 264, 334, 344, 346 class, 245 no lengthy processing, 264 matching, , 248, 260, 264, 302, 304, 342, 346 object, 241 output, 288, 290 target, , 260, 302, 304 template, , 248, 258, 260, , 290, 302, 304, 306, 337, 342 tuple space, 23, 26, , , , 252, 254, 256, 258, 263, tuple space cont. 268, 276, 288, 301, , 336, 344, 474, 484, 502, 510 see also communication central server, 249 conditional read, 245 conditional take, 244, 253, 270 get, 336 matching algorithm, 245 put, , 244, 248, 253, , , 268, 270, 272, 290, , 304, 312, , 322, 324, 331, 334, , 342, 346 read, , 249, 258, 264 separate for each job, 240 take, 240, , 248, 253, 256, 259, , 290, 302, 304, 306, 312, 318, 324, 331, Twitter, 4, 32 U unbalanced load, 100, 102, , 114, 278 see also load balancing uncoupled, 22-23, 26, 28, 240 see also coupling University of Texas, 514 user, 228 account, 274, 276, 286 directory, 286 files, 274 V variable global, 60, 62, 70, 72, 74, 76, 90, 92, 112, 130, 172, 174, , 208, , 270, 390, 392, 442, 508, 516 local, 176, 178 per-thread, 70, 72, 74, 76, 82, 88, 90, 92, 94, 98, 112, 128, , 204, 288, 322, 376, 378, 380, , 390, 392, 442, 474, 478, 484, 516 reduction, 70, 82, 84, 86, 90, 92, 94, 130, 163, 172, 174, 270, 276,

20 542 BIG CPU, BIG DATA variable cont. reduction cont. 324, 390, 392, 442, , 466, 468, 516 shared, 62, 74, 112, 214, 252 thread-local, 62, 66, 130, 174, 270, 508 WORM, 62 vector, 362, , 368, 414 class, 414, 416, 418 object, 414, 416 outer product, 356 structure, 414, 416, 418, 420, 422 method, 416 velocity, 126 velocity, 124, , , 402, 404, 416 Verizon, 482 vertex, , 168, 170, 182, , , , 204, 206, 210, 212, 324, 328, 330, 332, 334 see also graph vertex adjacent, , 206, 208 cover, 163, 172, 174, 187, 322, 324, 328 degree, 200 set, 163, 166, 168, 172, 174, 187, 190 set object, 176, 178 vertex cover, 192 minimum, , 172, 174, , 190, 192, 194 virtual machine, 249 volatile, 204, , 258 W WalkSat, 432 watts, 40 weak scaling, , 144, , 156, 186, 192, 194, 220, 274, 312, 316, 324, 328, 394, 518 Weak Scaling Law, 152 weak sequential fraction, 152, 154 weather station, 488 web browser, 98, 228 request, , 482 web cont. server, 4, 475 log analysis program, 475, 488, 500 log data, 474 log file, 476, 478, 480 site secure, 98, 348 work item, , 208, , 334, , 350 class, 332, 334 tuple, 331, 337 work queue, , 206, 208, 212, , 334, 336, 338 job, , 334, 336 pattern, , , 334, 348, 350 state, work sharing, see parallel loop worker, 259, 270, 274, , 288, 300, 302, 304, 312, 316, 319, 324 process, 278 rank, 302, 304, 306 task, , 256, , , 268, 270, 272, 274, 278, 280, 284, 286, 288, 290, 300, 302, 306, 312, 316, 319, 322, 324, , , 348, 350 class, 254, 256, 288, 304 main program, 272 WORM variable, 62 Write Once Read Many, see WORM variable Y Yahoo, 32 Z zombies, 124, 127, 136, 153, , 306, 310, 312, 316, 318 equilibrium state, 124, 126, 153 initial state, 124 position, 124, , 132, , 304, 306, , , 402, 404, 406, 408, 410, 416, 418 program, , 156, 158, 300,

21 Index 543 zombies cont. program cont , 398, 414, 416, 514 snapshot, 130, 132, 406, 408, 410 tuple, 302, 304, 306, 312, 316, 319 velocity, 124, , , 402, 404, 416

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